Gravity models have been widely used in expanded gaming debates to
persuade investors that proposed casinos will be financially successful
and to persuade state and local government officials, as well as a
skeptical public, of the economic and fiscal benefits of casino gaming.
However, most people involved in the decision-making process understand
very little about the internal mechanics of these models and how they
generate financial forecasts, estimates of customer visits, and
projections of new job creation. In fact, the gravity models used in
market feasibility studies for the casino industry are proprietary
models that remain closely guarded secrets of the industry and its
consultants. The purpose of this article is to open the use of gravity
models to critical scrutiny by reviewing their origins, development, and
limitations. A second purpose is to illustrate our main thesis by
analyzing gravity models deployed in the New England expanded gaming
debates. The authors offer a proposed modification to the calculation of
gravity factors to account for the growing importance of non-gaming
amenities.

Keywords: Gravity Model; Huff Model; Casino Industry

The Basic Facts of Expanding Gaming

In the United States today, there are 492 commercial casinos and
448 Indian casinos hosted by 37 states as compared to less than half
that number of casinos in two states in 1988 (AGA, 2013). However, after
twenty-five years of expanded gaming legislation at both the state and
federal levels, nearly half (46%) of all commercial casinos are now
located in non-traditional jurisdictions (i.e., outside Nevada and New
Jersey) and, if one includes Indian casinos, then seventy-two percent
(72%) of all U.S. casinos are now located in non-traditional
jurisdictions (AGA, 2012, pp. 12-22; Meister, 2012, pp. 15, 73). The
percentage of adults who gambled at a casino at least once in the
previous year climbed from 17 percent in 1990 to 32 percent in 2012,
when 76.1 million Americans made more than 400 million visits to casinos
(Harrahs, 2006; AGA, 2013, p. 3). Moreover, since the early 1990s, when
new casinos began opening in non-traditional jurisdictions, nearly 82
percent of the increase in casino visitations has occurred in
non-traditional casino jurisdictions, which now also account for 49
percent of casino gross gaming revenues (GGR) nationally. If Class III
Indian casinos are factored into the equation, non-traditional venues
now account for 69 percent of casino GGR nationally (AGA, 2012, pp.
1222; Meister, 2012, pp. 15, 73).

During this time, the debates over expanded gaming from state to
state have been remarkably similar because its proponents have offered
the same two rationales for policy change in every jurisdiction: new tax
revenues and economic development (i.e., jobs) (Evart, Treptow, and
Zeitz, 1997, p. 425). The same two rationales structure debates about
individual casino projects regardless of their type or location. Casino
revenue and operating forecasts, as well as projections of new job
creation, are normally based on market feasibility studies that depend
on gravity models. Government officials want to know how much tax
revenue proposed casinos will generate, while citizens want to know how
many and what types of new jobs will be created by a casino. Chambers of
commerce and restaurant associations are often concerned about the
potential impact of casinos on the local lodging, food and beverage, and
retail sectors. Tourism officials, and other segments of the hospitality
industry, demand reliable estimates of the number of out-of-region
visitors that can be generated by casinos and how many visits and what
type of spending will occur each year as a result of those visits.

Thus, one purpose of gravity models has been to provide investors
with an evaluation of specific sites for proposed business
establishments and to determine the potential sales of the proposed
establishments within a reasonable range of error, which allows
investors to assess the probability that the proposed casino will be
financially successful. A second practical use of gravity models has
been to provide investors with empirically based research that allows
them to identify the best location among alternative possible locations
for particular casinos, with the 'best" location being the one
that "will produce for the firm an optimum share of the market
potential, a minimum hazard for future sales erosion, and a maximum
return on total investment over the long-run" (Applebaum, 1965, p.
235). A third use that is not unique to the casino industry is
persuading state and local government officials, as well as a skeptical
public, of the economic and fiscal benefits of expanded casino gaming.

However, John Williams (1997, p. 402) observes that outside of
Nevada and New Jersey, where casinos have operated in fairly
well-defined markets, any "feasibility study requires an intuitive
leap from the known into the unknown," because "there is no
magic formula by which you add A, B and C and reach X as a casinos
performance." Yet, this is exactly the function of gravity models
in market feasibility studies, even though most people involved in the
decision-making process understand very little about the inputs to a
gravity model and much less about the internal mechanics of these models
and how they generate financial forecasts and estimates of customer
visits (Hashimoto and Fenich, 2007, p. 47). In fact, scholars have often
criticized gravity models as a black box (Bucklin, 1971, p. 490)--one
can observe what goes in and what comes out--but not how inputs are
converted into outputs. Despite this theoretical criticism, gravity
models continue to be utilized and refined by private consultants and
university scholars primarily on pragmatic grounds, i.e., because they
seem to generate reasonably accurate revenue forecasts that public and
private decision-makers find persuasive (Huff, 1963, p. 81; Evenett and
Keller, 2002)

The gravity models used in most market feasibility studies for the
casino industry are proprietary models that remain closely guarded
secrets of the industry and its consultants. For instance, the
International Gaming Institute (IGI, 1996) at the University of Nevada,
Las Vegas (UNLV) published one of the first introductory overviews of
the post-Las Vegas/Atlantic City casino industry in 1996 following the
rapid expansion of riverboat and dockside gaming in the Mississippi
River states and the introduction of racetrack casinos in the Northeast.
This introduction to "the gaming industry" covered the
historical background, economics, operations, and management of casinos,
but without any mention of the role that market feasibility studies had
played in each states expanded gaming debates.

John Williams (1997, p. 402), who was one of the first to discuss
this issue in the newly emerging gambling studies literature offered a
generic discussion of the importance of market feasibility studies, but
"without going into detail about all the methods of homing in on a
market." Similarly, and more recently, Douglas Walkers (2007, pp.
5-34) highly respected The Economics of Casino Gambling examines the
relationship between casino gaming and economic growth, including an
extensive analysis of various methodological debates, but the book does
not contain a single reference to gravity models and this omission is
replicated in Walkers Casinonomics: The Socioeconomic Impacts of the
Casino Industry (2013). Likewise, Kathryn Hashimoto's recent book
on Casino Marketing (2010, pp. 16-21, 41) discusses the role of
strategic planning and consumer behavior in casino marketing, but it
does not discuss the role of gravity models in initial revenue
forecasting or their importance to the industry's business and
political practices.

In fact, a JSTOR search of journals in business, economics,
finance, management, marketing, and transportation studies found exactly
one published reference to the use of gravity models in gambling studies
since 1931 (the origin of the gravity model) despite there being 367
total references in the academic literature to the use of gravity models
in other industries. A Google.com key word search discovered one
PowerPoint presentation delivered at the 13th International Conference
on Gambling and Risk faking (Cummings, 2006). Nevertheless, during the
last twenty-five years, gravity models have played a prominent role in
persuading public officials to authorize expanded gaming in the United
States, and elsewhere, and they have supported private decisions by
casino operators, banks, and other financial institutions to invest in
expanded gaming at various locations.

Thus, the purpose of this article is to open the use of gravity
models to critical scrutiny by reviewing their origins, development, and
limitations, particularly in light of recent changes in the casino
industry. A second purpose is to point out the limitations of current
gravity models in evaluating contemporary gaming markets and to propose
a modification to the so-called gravity factor used in these models so
they better account for the growing importance of non-gaming amenities.

Reilly's Law of Retail Gravitation

The gravity model is a tool first developed by economists in the
late 1920s and early 1930s for the purpose of estimating retail trade
flows between various geographic areas, although private retail
companies quickly recognized their utility for estimating the potential
customer base and future annual sales of new stores. Gravity models are
actually derived from Sir Isaac Newtons Law of Gravitation, which was
first used to predict the movement of people, commodities, and sales by
William J. Reilly, a professor of business at the University of Texas.
(1) Reilly published The Law of Retail Gravitation in 1931 after he
realized that Newtons Law of Gravitation seemed to loosely express the
empirical regularities he observed while conducting several trading area
investigations for chain grocery stores in Texas during the late 1920s
(Reilly, 1929). (2)

Newtons Law of Gravitation, which was first articulated in his
Philosophice Naturalis Principia Mathematica (1687) states that the
gravitational force between two masses is proportional to the product of
the two masses and inversely proportional to the square of the distance
between them. Reilly argued that Newtons Law of Gravitation seemed to
provide a good working hypothesis for defining the boundaries of
competing retail trade areas if one translated the law into two
behavioral concepts: (a) that the ability of a city to attract
non-resident trade is a function of its population (mass) and (b) that
the flow of nonresident trade to a city is an inverse function of
distance (force) (Thompson, 1967, p. 37). If one adopted this
hypothesis, then the law of retail gravitation could be used to
calculate the breaking point" between two places, where customers
will be drawn to one or another of two competing commercial centers
(Anas, 1987, pp. 45-54; Golledge and Timmermans, 1988). In this sense,
Reilly argued that "two cities attract retail trade from an
intermediate city or town in the vicinity of the breaking point
approximately in direct proportion to the populations of the two cities
and in inverse proportion to the square of the distances from the two
cities to the intermediate town" (Huff, 1963, pp. 81-82), although
notably, Reilly's formulation of the law presumes that the
geography of an area is flat without any rivers, roads, or mountains to
alter a (consumer's decision about where to travel to purchase a
particular good or service.

Reilly's Law remained an interesting hypothesis for more than
a decade and, as late as 1944, the editor of The Journal of Marketing,
which became a key academic testing ground for Reilly's Law, wrote
that there is a real need for inductive studies of consumer buying
habits" (quoted in Bennett, 1944, p. 405). Professor Victor W.
Bennett published one of the first studies of this type based on a
survey of 240 families living in Laurel, Maryland. The families were
questioned on their choice of shopping venues in Baltimore, Maryland and
Washington, D.C. and, in one of the first empirical tests of
Reilly's Law, Bennett (1944, p. 413) found that "there is more
out-of-town buying by Laurel consumers in Baltimore than in Washington,
[which] conforms roughly to the application of Reilly's Law.

Bennett's study was followed by the noteworthy work of P.D.
Converse (1943; 1946; 1948), a professor of business at the University
of Illinois, who examined retail customer movement between several
communities in Illinois and established the usefulness of Reilly's
Law for defining retail trade areas across a much larger geographic
area. However, Converse (1949) made a significant addition to
Reilly's Law that more precisely determined the breaking point
between competing trading areas centered in two different cities.
Converse defined the breaking point between two trading areas as an
equilibrium boundary line where [B.sub.a] = [B.sub.b] i.e., the point up
to which one city exercises a dominant trading influence and beyond
which another city dominates. The mathematical version of this
adaptation is:

(Equation 1)

[B.sub.ab] = [D.sub.ab]/1 + [square root of [P.sub.a]/[P.sub.b]

Where

[B.sub.ab] = the breaking point between city A and city B in miles
from B

[D.sub.ab] = the distance separating city A from city B

[P.sub.a] = the population of city A; and

[P.sub.b] = the population of city B

This breakthrough was followed by the work of Frank Strohkarck and
Katherine Phelps, who were working for the Curtis Publishing Company.
They authored a 1948 article on the mechanics of constructing a trade
area map that for the first time visually represented competing trade
areas as a series of concentric and overlapping circles emanating from
central places much like the three dimensional topographical or contour
maps familiar to geographers. Thus, Strohkarck and Phelps added an
important cartographic dimension to the gravity model as well as a
mathematical refinement of the breaking point concept.

The pioneering work of Strohkarck and Phelps was further refined by
Edna Douglas (1949a; 1949b), who employed three methods for identifying
retail customer origins in Charlotte, North Carolina: (1) the records of
the Credit Bureau of the Charlotte Merchants' Association to
determine customers addresses, (2) checks deposited during one week by a
group of local retail stores to determine the location of the banks
against which they were drawn and (3) an origin-destination study of
passenger cars leaving Charlotte. Douglass (1949b, p. 60) findings
reinforced previous studies and again found that Reilly's law of
retail gravitation provides a remarkably accurate delineation of the
Charlotte retail trading area." However, Douglas's empirical
findings also suggested a slight modification to Strohkarck's and
Phelps' concept of concentric market areas.

First, Douglas (1949b, pp. 59-60) found that the retail trading
area was not a single concentric circle with one breaking point, but a
series of circles within circles that comprised primary, secondary, and
tertiary market areas, with customers in the tertiary market coming from
otherwise significant trading areas that were in competition with
Charlotte. This led Douglas to conclude that market breaking points were
not hard boundaries, where all the potential customers on one side
gravitated in one direction and all of those on the other side
gravitated in the other direction, but porous boundaries that delineated
points where an exponentially decreasing proportion of customers would
be drawn to a trading area. In this formulation, the Strohkarck and
Phelps breaking point formula defines the outer boundary of a primary
market area at which point the proportion of customers attracted to a
trading area begins to decline exponentially, while the tertiary market
area marks another point of exponential decline in customer attraction
(force), because the gravitational pull of a competing, but closer
trading area begins to exert greater force on customers. Douglas also
found that the primary market area was indeed nearly circular as
hypothesized by Strohkarck and Phelps, but the secondary market area
became somewhat elliptical, while the boundaries of the tertiary market
area were quite erratic depending upon the level of competition from
outlying areas with significant trading centers.

The next major advance in gravity modeling was stimulated by the
emergence of regional shopping centers (i.e., malls). By the 1950s, the
investors in costly real estate projects, such as banks, insurance
companies, and other financial institutions, were no longer willing to
rely on the intuition of business entrepreneurs for making decisions,
but increasingly sought to base investment decisions on solid factual
information as to the profitability of a proposed real estate
investment. Similarly, prospective store tenants, often the large retail
chains that were being asked to anchor the shopping centers, conducted
their own studies to evaluate proposed shopping center locations. This
second generation of trade area studies incorporated concepts and
research techniques from marketing, geography, statistics, economics and
the behavioral science disciplines (e.g., psychology and sociology)
(Applebaum, 1965, p. 234). By the mid-1950s, this type of gravity model
was being applied to both inter-urban and intra-urban market areas for
the purpose of determining the market feasibility ot local malls, large
chain stores, and regional shopping centers (Ellwood, 1954) and by the
1960s gravity models were being used to assist government officials with
economic development and urban planning (Huff, 1963; Lakshmanan, 1964).
Subsequently, gravity models were used to predict consumer preferences
for a wide variety of competing retail and service industry outlets,
such as hospitals (Bucklin, 1971), large chain stores (MacKay, 1973),
banks (Ali and Greenbaum, 1977), and movie theatres (Davis, 2006). By
the 1970s, gravity models were being extended to the leisure and social
travel industries (Gilbert, Peterson, and Line 1972; Stutz 1973;
Vickerman 1974).

However, during this period (1950-1970), there were two additional
developments in the science of gravity modeling. First, as Louis P.
Bucklin (1971, p. 489) observes: "In its original formulation, the
retail gravity model was used to predict the point between two cities
where trade between them would be divided. This 'breaking
point' defined the geographical size of the market which each city
controlled vis-a-vis the other." However, Bucklin (1967a; 1967b)
was among the first scholars to test the gravity models ability to
predict intra-urban shopping patterns as opposed to inter-urban shopping
patterns. For example, in one study, Bucklin conducted a survey of 500
female heads of household in Oakland, California. In this study, he
(1967b, p.42) concluded "that mass retains much influence in the
selection of an intra-urban shopping center," but this innovation
also shifted the concept of mass from the size of an areas population to
the size and composition of the facility. This subtle shift built on the
work of Professor George Schwartz's (1963) University of Illinois
marketing group, which had generated impressive statistical evidence to
validate Reilly's original hypothesis that one could use population
or retail square footage as the sole proxy for measuring retail mass in
gravity models.

The results of these studies were so consistent and so reliable
that nearly three decades after the publication of Reilly's Law of
Retail Gravity (1931), Robert Ferber (1958, 302) was able to declare
that: "The two variables included in Reilly's Law and in
subsequent formulations--population, and distance--account for almost
all the variations in sales between cities."

Indeed, after three decades of testing Reilly's Law, Allen F.
Jung (1959, p. 62), a research associate at the University of Chicago
suggested that "through the years little, if any, evidence has been
presented which conflicts with this [Reilly's] law.' These
claims were reaffirmed by David L. Huff (1963, p. 81), who observed that
empirical evidence is available to indicate that in many cases the use
of such [gravity] models has provided fairly good approximations of the
limits of a number of retail trade areas."

The Huff Model: Variety, Time, Income, and Probability

Scholars, retail executives, real estate investors, and urban
planners enthusiastically embraced Reilly's Law of Retail
Gravitation as an iron law of retail trade distribution, but at the same
time a number of methodological amplifications were introduced in the
1960s and 1970s which culminated in the introduction of the "Huff
model" (Applebaum, 1965, p. 234). It is actually David L. Huff, a
former professor of business at the University of California, Los
Angeles (UCLA), who pioneered the type of gravity model utilized most
frequently by the casino industry and casino industry consultants. Huff
(1963, 85) proposed four modifications to Reilly's Law that were
critical to the development of the Huff model: (1) Merchandise Offerings
(or the number of items of the kind a consumer desires that are carried
by the retail outlet), (2) the travel time that is involved in getting
from a consumer's travel base to alternative retail facilities, (3)
the average household income of people living in the trading area, and
(4) probability contours as opposed to breaking points. We might suggest
by way of analogy! that just as Newtonian mechanics was
superseded--though not displaced--by Niels Bohrs quantum mechanics a
similar phenomenon occurred in the business and social sciences as the
focus shifted from aggregate populations to individual consumer
behavior--or from planetary bodies to sub-atomic particles.

First, Huff suggested that it is not just the square footage that
measures the mass of a retail facility, but rather square footage is
really a proxy indicator for the number of stores, types of stores, and
range of merchandise offerings at a particular location, because it is
this variety that justifies traveling longer distances by making more
purchasing options available at a single location. In the gravity models
used by the casino industry and its consultants, this concept of mass
has typically been operationalized exclusively in terms of gaming
positions, where one slot machine equals one gaming position and one
table game equals five or six positions, because a table can accommodate
multiple players. (3) These accumulated modifications to the concept of
mass are often referred to today! as "destination effects"
(Black, 1983).

Second, and despite widespread recognition of this shortcoming,
most gravity models, including those used in the casino industry are
based on the assumption that customers patronize a facility according to
some rule involving the comparative distance between two facilities, all
other things being equal. A customer prefers facility A over facility B
if the distance to facility A is shorter than some function of the
distance to facility B (Drezner, Drezner, and Eiselt, 1996). However,
Richard Nelson (1958, p. 149) was one of the first scholars to suggest
that driving time, rather than distance was a more important determinant
of customer preference for alternative shopping facilities (Nelson,
1958, p. 149). Similarly, by the late 1950s, Eugene J. Kelley (1958, p.
32) had commented that "convenience costs are assuming more
importance as patronage determinants compared to distance. Kelley
observes by this time that marketers had actually identified "ten
convenience forms" with "place convenience" being only
one of the ten forms. Nevertheless, Kelley's work continued to
emphasize the importance of place, or geographic area, as defined by the
concentration or dispersion of population as did Reilly.

Yet, Kelley did introduce two new elements into the concept of
place convenience. Kelley (1958, p. 35) challenged the equivalence of
"the distance concept" with "convenience" by noting
that distance involves "time-cost elements rather than a purely
spatial one." Higher road speeds and the emergence of large planned
retail centers were actually changing consumers' perceptions of
distance, because one could travel further faster and obtain more goods
and services at a single location. Kelley (1958, p. 35) also noted the
importance of parking to retail structures as an element of time
convenience, observing that "it is generally agreed that shoppers
resist walking more than 600 feet from their parked cars to the nearest
center store...this suggests a limit to the maximum parking distance
that can be used before a retail center loses its other advantages over
competing centers and certainly anyone who operates, manages, or visits
a casino will recognize the importance of parking, i.e., finding a space
quickly, getting into the facility quickly, and avoiding inclement
weather.

Kelley's observation was validated in subsequent research,
including a study by Professors James A. Brunner and John L. Mason
(1968), who studied consumer preferences for various shopping centers in
Toledo, Ohio based on drive-times as opposed to distance. The findings
confirmed the drive-time hypothesis as superior to the simple distance
concept proposed by Reilly, but given the limited geographic sample,
Brunner and Mason (1968, p. 61) called on other researchers "to
ascertain the degree to which these observations are generally true for
other shopping centers in other communities." A license plate
survey of 93,500 passenger cars in 18 Greater Cleveland shopping centers
by Cox and Cooke (1970, p. 13) in fact confirmed that "the driving
time required to reach a center is highly influential in determining
consumer shopping center preferences (also see, McCarthy, 1964, p. 577;
Cox and Erickson, 1967, p. 52; Berry, 1967).

However, Cox and Cooke also found that the "drawing power
(i.e., gravity factor) of a shopping center still had to be incorporated
into the gravity model, because consumers were willing to drive farther
to reach a shopping center depending upon "relative
attractiveness" compared to other shopping centers. Cox and Cooke
(1970, p. 14) suggested that a number of factors could be used to
measure the attractiveness of a facility, such as the number of parking
spaces, the size of the center, and the types of stores in the
center," since these factors could partially overcome the friction
or inertia of drive-time and distance. Furthermore, Gautschi (1981)
points out that the first gravity models constructed to evaluate the
potential trade areas of planned shopping centers assumed the automobile
of the 1950s and the 1960s, as well as the transportation network in
place at the time. Consequently, Gautschi (1981, p. 172) argues that the
development of better, faster, and more comfortable automobiles, the
construction of superior road systems (parkways, interstate highways),
and urban mass transit means (at least theoretically) that "the
travel time parameter has an inflated absolute value," which
"serves to underestimate the expanse of a center's trading
area."

However, even as late as 1978, Raymond Hubbard found that "the
vast majority of the literature" on gravity modeling and retail
trade areas still utilized "objective distance data," rather
than drive times partly because distance data was easily available, but
drive times were not available in any readily useable format. The use of
distance, rather than drive-time, has been almost universal in the
casino industry's gravity models, but the difference between
distance and drive-time can be significant in various geographies that
are not flat, where the width and quality of roads is not consistent,
where weather can be a factor, and where urban congestion or other choke
points can significantly alter the relationship between distance and
drive-time. However, the lack of available data on drive-times is a
technical problem that should largely have been eliminated by the
introduction of computer and internet programs, such as MapPoint, Google
Maps, Yahoo Maps, Map Quest, Free Mileage Calculator, and other programs
that have made drive-time data easily accessible for incorporation into
gravity models.

Third, while Reilly accounted for differences of population, he did
not account for differences of income. Yet, as early as 1958,
Ferber's (1958, p. 303) consumer behavior research, which was based
on Reilly's Law had found that income is a major factor influencing
variations in per capita retail sales between cities for most categories
of sales." Similarly, Bucklin (1967b, p. 42) found that consumer
perceptions about the value mass imparts vary considerably" among
consumers depending on the motivation of consumers. In particular, he
found that mass had a higher attraction (force) for those with higher
incomes, since these consumer cohorts were willing to travel farther to
a primary retail center to obtain the benefits of retail mass, while
secondary centers held a greater attraction for those seeking
convenience, and tertiary centers (i.e., small out of the way stores)
were more likely to attract price conscious consumers. Thus, subsequent
research has found that mass and income are two factors that will
interact to promote "excess travel behavior" (Hubbard, 1978,
pp. 8-10). This is not only because a larger mass exerts more
gravitational force on consumers, but because "those individuals
showing evidence of higher income levels are more readily able to bear
the costs involved in shopping around, and therefore tend to travel
greater distances in the journey to consume (Hubbard, 1978, p. 9; for
example, McAnnally, 1965; Schiller, 1972). Thus, a larger and more
attractive retail facility increases the likelihood that higher income
consumers will travel distances in excess of those that are
theoretically justified (Hubbard, 1978, p. 9). By the late 1960s,
consumer behavior surveys were documenting that the nearest center
postulate "provided an inadequate description of consumer
movements" and that large numbers of consumers deviated from what
was defined as spatially lawful behavior" (Golledge et al., 1967;
Rushton et ah, 1967; Hubbard, 1978, pp. 3-4). This is particularly
important to gravity modeling in the casino industry, where surveys have
documented that the individuals who patronize destination resort
casinos, in particular, have incomes higher than the median income of
its host jurisdiction (AGA, 2013; Barrow and Borges, 2011).

Finally, David L. Huff (1961, p. 84) identified another significant
limitation to the application of Reilly's Law, which is that the
calculation of breaking points to delimit a retail trade area conveys an
impression that a trading area is a fixed boundary circumscribing the
market potential of a retail facility, when in fact there is an
exponential distance decay factor of declining retail attraction within
the trade area, as well as interpenetration and overlap between
designated market areas." This problem had been identified earlier
in the development of gravity modeling by scholars, such as Edna
Douglas, who had mapped trade areas based on actual consumer origins,
rather than distance postulates. Huff (1961, p. 490) built on this work,
but was more emphatic in stating that trading areas do not have hard
boundaries, but shade off into one another and, therefore,
"probabilistic models are appropriate measures of this process.
Thus, Huff proposed that breaking points be replaced by "exponents,
which are the statistical units that capture and measure the distance
decay factor in terms of the probability that an individual consumer
will choose to patronize a specified facility (Huff and Jencks, 1968).
This does not mean that the breaking point formula is irrelevant, but
that it defines the 0.50 probabilistic contour or the point up to which
a customer has a greater or less than fifty percent (50%) probability of
selecting one facility over another. The lines demarcating or connecting
the geographical units with comparable decay factors on a map are called
"probability contours" instead of market boundaries, because
they delimit the statistical probability that individuals will select a
particular trading area or facility.

The "most obvious deficiency" in the application of this
principle at the time was "the lack of direct information on the
actual spatial movements and expenditures of individuals" (Golledge
et al., 1966, p. 261). This difficult has largely been removed in the
casino industry where the annual Harrahs (2006) surveys of
"propensity to gamble"--now conducted by the American Gaming
Association (2007-2013)--has provided reliable data at the state level.
The development of sophisticated players' club databases, hotel
guest databases, and daily headcounts by casinos have perhaps made the
industry a leader in this area, particularly as this proprietary
information is often provided to consultants, who can then develop more
I elaborate models based on actual player origins and gaming behavior
(e.g., spend per visit).

The Huff model, which was first articulated in two articles
published I in 1963 and 1964, incorporated these four modifications to
Reilly's Law to construct an alternative model of retail
gravitation based on consumer behavior theory and goods theory, rather
than central place theory. In Huffs (1963, pp. 87-88) article, he walks
the reader through a seven step process for constructing a gravity model
that incorporates drive times and that maps trade areas based on
exponential decay factors, the actual population residing within these
probabilistic contours, and the average household income of the
households residing within each contour of the map. The seven step
process for constructing a Huff models is as follows:

1. "Divide the area surrounding any existing or proposed
shopping center into small statistical units. These units could be
Census enumeration districts.

2. Determine the square footage of retail selling space of all
shopping centers included within the area of analysis.

3. Ascertain the travel time involved in getting from a particular
statistical unit to each of the specified shopping centers.

4. Calculate the probability of consumers in each of the
statistical units going to the particular shopping center under
investigation for a given product purchase.

5. Map the trading area of the shopping center in question by
drawing lines connecting all statistical units having like
probabilities.

6. Calculate the number of households within each of the
statistical units. The, multiply each of these figures by their
appropriate probability values to determine the expected number of
consumers (expressed in households) who will patronize the shopping
center in question for a particular product purchase.

7. Determine the annual average per household incomes of each of
the statistic units. Compare such figures to corresponding annual
household budget expenditures in order to determine the average expected
amounts spent by such families on various classes of products, e.g.,
clothing and furniture. Estimate annual sales for the shopping center
under investigation by multiplying each of the product budget figures by
expected number of consumers from each statistical unit who are expected
to patronize the shopping

center in question. Then, sum these individual estimates to arrive
at a total annual sales potential by product class for the selected
shopping center" (Huff 1963, 87-88).

With respect to Step 6: Huff (1963, p. 87) notes that "in
addition to the likelihood [propensity] of consumers from various
statistical units patronizing a proposed shopping center, it is
necessary to know the expected number of such consumers from each of the
units. For example, it might be that a given contour possesses a high
probability value but the consumers within its confines may be few in
number and, therefore, provide few customers and little revenue to the
proposed facility. Similarly, with respect to Step 7, Huff (1963, p. 88)
observes that "in terms of purchasing potential, another contour
possessing a much smaller expected number of consumers may have a
greater disposable income level and thus greater purchasing
potential."

A formal expression of the Huff (1964, p. 36) model is:

(Equation 2)

[P.sub.ij] = [S.sub.j]/[T.sub.ij][DELTA]

[n.summation over (j=1) [S.sub.j]/[T.sub.ij][DELTA]

* where [P.sub.ij] = the probability of a consumer at a given point
of origin traveling to a particular shopping center j;

* Sj = the size of a shopping center j (measured in terms of the
square footage of selling area devoted to the sale of a particular class
of goods);

* [T.sub.ij] = the travel time involved in getting from a
consumer's travel base I to a given shopping center j; and

* [DELTA] = a parameter which is to be estimated empirically to
reflect the effect of travel time on various kinds of shopping trips.

As Huff (1964, p. 36) described it, the expected number of
consumers at a given place of origin i that shop at a particular
shopping center j is equal to the number of consumers at i multiplied by
the probability that a consumer at i will select j for shopping.

That is:

(Equation 3)

[E.sub.ij] = [P.sub.ij] * [C.sub.i]

* where [E.sub.ij] = the expected number of consumers at i that are
likely to travel to shopping center j; and

* Ci = the number of consumers at i.

Huff (1964, p. 36) noted that his model "resembles the
original model formulated by Reilly" but he argued that it differed
from Reilly's Law of Retail Gravitation "in several important
respects." The most important theoretical difference is that Huffs
(1964, pp. 36-37) model was not a "contrived formulation"
designed post-hoc to describe observed empirical regularities, but a
theoretical abstraction of consumer spatial behavior." As a result,
real data including population, average household income, square
footage, drive times, and propensity factors can be used in mathematical
calculations to deduce probabilistic conclusions about the number of
consumers and the spend per consumer that for a particular type and size
of retail facility.

Gravity Models and Casino Gaming

The first likely use of gravity modeling as a means of forecasting
casino revenues was by Economics Research Associates (ERA), an economics
consulting firm, which produced a study in 1976 on the potential
economic and fiscal impacts of legalized casino gaming in Atlantic City,
New Jersey. The ERA study was released into a highly charged political
atmosphere, since the forecasts from the study were incorporated into
campaign literature developed by the Committee to Rebuild Atlantic City,
which at the time was the states leading pro-gaming coalition (Heneghan,
1999, p. 119). The models forecasts evidently proved persuasive because
the New Jersey referendum passed, but the ERA model immediately revealed
both the promise and the shortcomings of gravity modeling in the casino
industry.

As a model designed to forecast revenues from a regional base of
commuter shoppers, it proved ill-equipped to accurately estimate
visitations and revenues in a new industry, while comparisons to Las
Vegas proved misleading for a new type of gaming market. On the one
hand, as Dan Heneghan (1999, p. 120) points out: "the projections
proved to be way off, because the promises turned out to be extremely
conservative." ERA's projections on annual visitations proved
far too conservative with respect to the number of visitors, but far too
optimistic on the length of stay by visitors, partly because Las Vegas
was the only gaming jurisdiction at the time and it was not recognized
that Atlantic City would be designed as a new type of regional commuter
destination, rather than a site for integrated resort casinos. Atlantic
City became a regional commuter destination, rather than a national or
international destination, such as Las Vegas, but it was one that
happened to be in the middle of one of the most densely populated areas
of the United States. Similarly, the employment projections derived from
the ERA model "were so conservative that the low end [of the
employment projections] was passed by the end of 1980" (Heneghan
1999, p. 121). The same was true with respect to forecasts about tax
revenues and capital investment (Heneghan 1999, pp. 123-27). However,
the Atlantic City experience established a familiar pattern of critics
claiming that the industry consultants projections were exaggerated,
while in fact they proved far too conservative.

The difficulty of calibrating gravity models to a new industry,
where reliable comparative data and primary behavioral data were in
short supply, would be revisited many times over the next two decades,
particularly after the federal government passed the Indian Gaming
Regulatory Act (IGRA) in 1988 to provide a legal framework for the
expansion of tribal gaming across the United States (Rand and Light,
2006). At the same time, several states legalized commercial casinos,
including South Dakota (1989), Iowa (1989), Colorado (1990), Illinois
(1990), Mississippi (1990), Louisiana (1991), Missouri (1993), Indiana
(1993), and Michigan (1996). Thus, as expanded gambling took hold in the
United States, John Williams (1997) correctly argued that one of the
main areas of future research in gambling studies would be patronage and
revenue forecasts. Williams (1997, pp. 402-403) did not elaborate how
this research would be conducted, nor did he recognize that it would
mainly be conducted by private consultants, rather than university-based
scholars, but he did identify the specific data points and comparative
factors that would have to be incorporated into future visitation and
revenue models, including:

* population, demographics, and disposable income,

* existing visitors, both domestic and international,

* ease of access to the casino, domestically and internationally,

* regional propensity to gamble and outlets for it,

* residents who go to other countries to gamble,

* limitations on opening hours, types of gambling and credit, and,

* the performance of other casinos in the region, from which some
parallels can be drawn.

Williams' recommendations might have provided the basis for a
I national research agenda for the growing number of scholars interested
in the gaming industry, but at least the casino industry's leading
economic consultants seem to have adopted variations of the framework
established by Williams (and even earlier by Huff). One could multiply
examples and I case studies endlessly, but a few examples from the New
England expanded I gaming debate are examined here to illustrate our
main thesis.

The first major wave of Indian and commercial gaming expansion into
non-traditional jurisdictions (1988-1996) ignited expanded gaming
debates in almost every region of the United States--the Mid-Atlantic
states, the Mississippi River Valley, the Upper Mid-West, the Rocky
Mountains, the Southwest, the Northwest, and New England. In New
England, the resounding success of Foxwoods Resort Casino in Ledyard,
Connecticut immediately set off what became a perennial expanded gaming
debate in almost every New England state with Massachusetts sitting at
the epicenter of that debate, because of its regional population and
wealth.

In Massachusetts, former Governor William Weld brokered a proposed
gaming compact in 1995 with the Aquinnah Wampanoag Tribe of Gayhead to
open a $200 million resort casino in New Bedford, Massachusetts
(Halbfinger, 1996). The Weld compact would have granted the Aquinnah
Wampanoag Tribe exclusive casino rights in eastern Massachusetts in
exchange for 25% of the casinos gross gaming revenues, while allowing a
limited number of slot machines at the states four racetracks
(Vaillancourt, 1994). A patron origin analysis released by the
University of Massachusetts Dartmouth estimated that Massachusetts
residents accounted for approximately 33% of Foxwoods' annual
visitations and that Massachusetts residents were spending at least $300
million per year gambling at Connecticut's billion dollar casino in
1995 (Dense and Barrow, 2003). Nevertheless, the Weld compact was
rejected by the state's House of Representatives.

In 1997, Governor Weld filed new casino legislation that would have
allowed the Aquinnah Wampanoag Tribe to operate one casino in New
Bedford, while authorizing a second casino in Hampden County (western
Massachusetts), and authorizing 700 slot machines at each of the
state's four racetracks. The governor's new bill died in
committee without a vote. However, the expanded gambling issue was
resurrected in 1999, when State Senator James P. Jajuga filed a bill
known as the Massachusetts Casino Control Act that would have authorized
the licensing of three resort casinos in Southeastern Massachusetts,
Western Massachusetts, and Northeastern Massachusetts, where voters in
each of the three regions had already passed non-binding referenda to
host a casino.

For the first time, and to bolster proponents' claims about
the potential economic impacts of the proposed casinos, a group of
business people in the western Town of Palmer known as the Committee for
Palmer Growth and Development hired Economics Research Associates to
prepare a Gaming Market Analysis for 3 Massachusetts Locations (1999).
Like each of the examples that follow, the ERA (1999, pp. 16-19) model
is semi-transparent insofar as it identifies the types of data
incorporated into the model (and often summarizes that data in tabular
form). The model incorporates total population, adult population (aged
21+), number of households, average per capita income, and aggregate
income in 30 minute drive time zones. The data is attributed to
Claritas, although ERA (1999, p. 16) "developed population and
income estimates for the resident population for drive times," and
then relies on these estimates "for estimating the market shares
between the casino locations." However, the equations and other
assumptions used to derive final estimates of demand (i.e., gross gaming
revenues), the weights assigned to various factors in the model (e g.,
drive-time), and the internal mechanics of the model are never specified
in the report. Moreover, the ERA (1999, pp. 3, 8-11) report never
specifies a comparative gravity factor for any of the proposed casinos,
but merely asserts that "the Massachusetts casinos would be of
sufficient size to compete with other casino offerings in the
northeast" in terms of slot machines, table games, and
"appropriate amenities."

In this case, Economic Research Associates (1999, p. 12)
operationalized a simple but standard gravity model. It uses drive times
as one means of estimating the potential numbers of adults 21 and over
who live within varying drive times distances from the three locations.
These [drive time bands] are broken into approximately half-hour
increments ... for purposes of approximating figures for attendance and
revenue." For purposes of estimating the number of annual casino
visits and forecasting revenues in a stabilized year, ERA (1999,18)
applies the national average (not locally specific) propensity to
gamble, including the national average trips per year to casinos
published in the Hurrahs Survey of Casino Entertainment (1996), although
as recommended by Walker, the report also makes comparisons to the
Atlantic City and Connecticut casinos to further calibrate revenue and
visitation estimates with purportedly comparable jurisdictions (ERA
1999, pp. 7-11). However, it does not appear that the model applies any
type of distance decay factor as would be required in a more
sophisticated Huff model. Finally, the ERA (1999, p. 18) report assumes
a 20% "Tourism Factor to account for nonI regional casino visitors
and revenues, based on Atlantic City bus arrivals, which is a typical
approach when confronted with this problem, because standard gravity
models cannot account for this type of visitor within their normal
parameters. The tourism factor is, in effect, a shot in the dark I an
educated guesstimate that could vary wildly from one jurisdiction to
another depending on location and the amenities necessary to generate a
destination effect. (4)

The ERA report concluded that three resort casinos distributed
across Massachusetts would generate 13.7 million annual visits and $1.1
billion in annual gross gaming revenue, but the 1999 Massachusetts
Casino Control Act was pigeonholed in a House committee and the expanded
gaming debate shifted to Rhode Island. In Rhode Island, a proposal by
Boyd Gaming Corporation and the Narragansett Indian Tribe to build a
$500 million destination resort casino was rejected by the Rhode Island
State Legislature in 2000 (Mello, 2000). However, soon thereafter,
Harrahs Entertainment, Inc. (now Caesars Entertainment, Inc.) and the
Narragansett Indian Tribe proposed a $600 million destination resort
casino in the Town of West Warwick, Rhode Island. Proponents of the
casino retained Christiansen Capital Advisors (CCA), which prepared a
report on the Potential Impacts of a West Warwick Casino: Draft Report
(2004). The CCA report (2004, 6) operationalizes a "supply
side" model, in contrast to the demand side model exemplified by
the ERA report, and states that "a convincing gauge of capacity
constraints" is "gaming revenue and win/unit/day" for the
facilities serving a gambling market." Based on comparative data
for the New England gaming market, the report (2004, p. 6) concludes
that "the observed distant adjusted spending per adult at the two
Connecticut casinos [i.e., Foxwoods and Mohegan Sun] and at the two
pari-mutuel facilities [i.e., Newport Grand and Lincoln], while
certainly respectable at $586.50 and an average of around $514
respectively, is lower than the rate of spending for similar facilities
in other more fully supplied jurisdictions." In the CCA (2004, p.
8) report, the "distant adjusted spending" at existing New
England gaming facilities, compared to national averages, provides the
basis for estimating "the demand for a casino to be located in West
Warwick, Rhode Island."

A follow up analysis entitled, Community Impacts of a Narragansett
Casino in West Warwick (2006, p. 1) examined a scenario in which a
casino resort facility with approximately 140,000 square feet of casino
floor, 150 table games of the kind offered at Foxwoods and Mohegan Sun,
3,500 slot machines and other gaming devices of the kind offered at
Foxwoods and Mohegan Sun, 500 hotel rooms, five restaurants, spa,
premium lounge and 55,000 square feet of meeting space is constructed...
in West Warwick, Rhode Island at an approximate total cost of $1
billion." This follow-up report (2006, pp. 1-7) contains a
statement of estimated revenues and visitations for the proposed casino,
but in this case there is absolutely no discussion of inputs and
methodology in what appears to be a standard gravity model and thus
decision-makers and the general public are left to take its findings on
trust and good faith in what is inevitably a highly charged and
politicized public debate. A referendum authorizing the proposed casino
was defeated 63% to 37% on November 7, 2006.

Following the six year expanded gaming debate in Rhode Island,
which resulted in three successive defeats for expanded gaming
proponents, the debate shifted back to Massachusetts when on October 11,
2007, Governor Deval Patrick filed legislation to authorize up to three
destination resort casinos in the Commonwealth of Massachusetts. In his
message to the State Senate and House of Representatives, Governor
Patrick indicated that the primary goal of his proposal was "to
spur economic development and job growth throughout the
Commonwealth" (Barrow, 2008). However, the governors revenue and
jobs projections were immediately dismissed by legislative critics, who
began calling for an "independent study" to review the
governors projections. In response, the Secretary of Economic
Development issued a competitive request for proposals that eventually
led to the hiring of Spectrum Gaming on February 22, 2008 as an
independent third-party firm with specific expertise in the gaming
industry." Spectrum Gaming was charged with examining the
saturation point for gambling in New England, generating revenue
projections based on the governors proposal, and estimating the
potential impact on the state lottery.

On August 1, 2008, Spectrum Gaming released its Comprehensive
Analysis: Projecting and Preparing for Potential Impact of Expanded
Gaming on Commonwealth of Massachusetts. The report (2008, p. 76)
contains two forecasts of estimated gross gaming revenues and annual
visitations:

"First, we look at the basic demand for the type of planned
destination casinos, absent any specific marketing programs that would
rely on hotel rooms to target and reward gaming customers. This allows
us to conservatively project the level of demand based on population
within a reasonable driving distance. Second, we follow that with
certain assumptions regarding the potential use of hotel rooms as
marketing tools to develop our revenue estimates."

In the first phase of the demand analysis, Spectrum (2008, pp.
77-78) operationalizes a standard gravity model that incorporates
"a variety of factors for each of these [three proposed]
properties, which we assumed to be in the center of each of these
[three] regions. These factors include, but are not limited to:

* Total population,

* Number of adults,

* The number and quality of competitors with in a two-hour drive,

* Number of slots and tables within that drive time,

* The type and quality of amenities of each competitor,

* Each competitors distance from center of each region,

* The gaming value of each region adjusted for household income
levels."

These factors are the typical inputs into a gravity model, but the
report immediately moves to a forecast of gross gaming revenues without
any further explanation of the model's internal mechanics, gravity
factors, weights, or calculations. The initial model's gravity
factor appears to be based exclusively on "the number of slots and
tables, since the report (2008, p. 79) deploys a second gravity model
that includes "the use of hotel rooms as marketing tools."
Yet, how this factor gets incorporated into, or appended onto, the
initial model is not explained in the repoit beyond the notion that by
setting aside 50% of hotel rooms as "comps" for preferred
players, it will add "incremental gaming revenue" above that
normally expected for a regional commuter facility (Spectrum, 2008, p.
81). Moreover, there is no discussion of whether or how "the type
and quality of amenities of each competitor' impacts revenues and
visitation estimates so despite claiming that these factors are part of
the model there is no explicit indication that these factors are
actually incorporated into the model or, if so, in what way.

The Massachusetts House of Representatives rejected Governor
Patrick's casino proposal on March 20, 2008 by a vote of 108 to 46.
However, following a change in legislative leadership, expanded gaming
again returned to the top of the state's legislative agenda. While
now generally supportive of the governor's previous gaming
proposal, the State Senate decided to update the previous economic and
fiscal analysis and commissioned a second report by the Innovation
Group, entitled Massachusetts Statewide Gaming Report (2010). The
Innovation Group (2010, pp. 86-87) tends to be more transparent than
most in the description of its gravity model for Massachusetts, which is
based on the identification of distinct market areas:

"Using our GIS software and Claritas database, the gamer
population [aged 21+], latitude and longitude, and average household
income is collected for each postal code. Each ot these market areas is
assigned a unique set of propensity and frequency factors ... both
propensity and frequency are inversely related to travel time to a
casino. In other words, as travel times increase, both the percentage of
persons who gamble and the number of times they visit a casino tend to
decrease. Gaming behavior also varies based on the availability and
quality of the gaming experience. Alternative forms of entertainment are
also a factor in determining gaming behavior. For this analysis,
propensity and frequency rates for each market area are based on survey
data presented earlier in this report and extrapolating information
provided in public filings and published reports on gaming behavior in
the region. Gamer visits are then generated from postal codes within
each of the market areas based on these factors and distributed among
the competitors based upon the size of each facility, its
attractiveness, and the relative distance from the postal code in
question. The gravity model then calculates the probabilistic
distribution ot gamer visits from each market area to each of the gaming
locations in the market."

The Innovation Groups gravity model incorporates the standard
factors, including adult population, average household income, drive
time, average propensity to gamble, and the availability and quality of
competing facilities. As with most such models, one can infer that some
variation of the standard Huff equations are used to derive revenue and
visitation estimates. Yet, the generic description of the model appears
to incorporate attractiveness" and "quality of the gaming
experience," which suggests that factors other than gaming
positions are being incorporated into the model as part of its gravity
factor. However, when one examines a methodological section entitled
Attraction Factors, which "measure the relative attraction of one
casino in relation to others in the market," one finds that
"attraction factors are applied to the size of the casino as
measured by the number of positions it has in the market. Positions are
defined as the number of gaming machines, plus the number of gaming
seats at the tables" (Innovation, 2010, p. 89). In other words,
slot machines and tables are the only measures of attractiveness (i.e.,
gravity).

One encounters a similar phenomenon in a response for proposals
(RFP) submitted to the Town of Plainville, Massachusetts by Cummings
Associates (2013), which includes examples of other gravity models
operationalized by the consultant. Despite another misfire in 2010,
Governor Deval Patrick finally signed a bill on November 22, 2011 that
authorizes three destination resort casinos and one slot parlor in the
state. Massachusetts is moving forward with the licensing process, which
requires potential casino operators to negotiate host community
agreements with local officials and to have that agreement ratified by
voters in a local referendum. The Town of Plainville, Massachusetts
already hosts a harness racing track, which is bidding on the one
authorized slot parlor license. To assist it in negotiating the host
community agreement, the Town of Plainville hired Cummings Associates
through a competitive bid process to prepare an analysis that includes a
gravity-model analysis of the likely market for the proposed
slot-machine facility at Plainridge" (Cummings, 2013, p.2).

Cummings Associates (2013, p. 6) states that "this type of
analysis is based on 'geography:' where do potential customers
live, and how far (or more accurately, how long) do they have to travel
to visit any existing or prospective casino that might be convenient for
them? The basic assumption of the gravity model is that other things
being equal, the surrounding population will tend to patronize each
facility at rates similar to those elsewhere" (Ibid., p. 13). In
their proposal to the Town of Plainville, Cummings notes that "a
description of this methodology and assessment of some of its finer
points may be found in several of the papers and PowerPoint
presentations I have delivered to several of the International
Conferences on Gambling and Risk-Taking, where the principal
investigator (2006) has documented that a casinos gravity is "not
always according to Reilly."

In an exemplary work submitted as part of the proposal, Assessment
of the Value of A License for a New Casino in Davenport, Iowa (July 21,
2008), Cummings' (2008, p. 2) concurs with CCA that the "Slot
Win/Unit/ Day" figure is a common measure of performance in the
casino industry, because slot machines typically provide 90%+ of the
revenues (and even more of the profits) of most regional casinos."
Thus, Cummings (2008, 2) argues that "slot performance is usually
the single most revealing measure of such performance." However,
Cummings adds another level of sophistication to this measure by
developing what he calls a casinos Power Rating (i.e., a type of gravity
factor), which measures a casino's ability to draw consumer
spending from the surrounding population by comparing the number of slot
machines at competing facilities and the win per unit per day at
competing facilities (Cummings 2008, Exhibits 6-13). The Cummings (2008,
p. 2) Power Rating indicator takes:

"the spending of the average adult who lives within the market
of each casino at its slot machines, and compares it to a benchmark
average of $700 per adult per year (who lives within ten miles of that
casino, adjusted for distance and competition). A power rating of 100
therefore represents average spending of $700 per adult (again, adjusted
for distance and competition)."

Cummings observes that a casinos Power Rating is similar to, but an
extension of, the "Fair Share" concept pioneered by Larry
Klatzkin and that is now used by many casino analysts. The Fair Share
concept is that if a casino has 20% of the slots within a market, but
attracts 22% of the slot revenues, it is attracting 110% of its fair
share" of the market, although Cummings (2008, p. 2 fn. 3)
"extends this element of comparison not just with other casinos in
the area but also with the size and distribution of the surrounding
population. However, despite being a model of transparency, when one
examines the tables and exhibits where the Power Ratings are defined,
the power ratings tables suggest that table games, hotel rooms, and even
attractiveness are components of the power rating, but in fact the
Cummings Power Rating is still based entirely on slot machines.

Analysis and Conclusion

There has been almost no academic literature on gravity modeling in
the casino industry, although a number of well-established and reputable
consulting firms have developed proprietary gravity models, including
Economics Research Associates, Spectrum Gaming Group, The Innovation
Group, Christiansen Capital Advisors, Wells Gaming Research, Cummings
Associates, and many other management and financial consulting firms. In
these gravity models, the problem of transparency is at least partially
resolved by assuming that these models use some version of the Huff
equations, including distance decay factors (i.e., drive times and
propensity to gamble), although in some earlier models this was clearly
not the case. Moreover, it is clear that greater sophistication has been
introduced into these models over time as it became possible to use
towns and cities, zip codes, census county divisions, or census blocks
as the geographic units for population and income. The geographical
units might vary depending on the political jurisdictions in different
parts of the country or the availability of prepackaged commercial
databases (e.g., Claritas, ESRI), but improvements in data availability,
comparative jurisdictions, and access to players club data have no doubt
improved the overall reliability of gravity models.

Likewise, official government data on disposable personal income,
per

capita income, and average household income for these units of
analysis has become more easily available as a result of CD-ROMs, the
internet, and the commercial repackaging of public data. Spreadsheet

programs, a user-friendly Statistical Package for Social Sciences
(SPSS), and other statistical software packages, coupled with rapid
developments in personal computing power have made it possible to
construct gravity models with tens of thousands of individual data
points that can be linked together in mathematical formulas.
Expectations about spend per visitor and the propensity to gamble are
now based on behavioral surveys, proprietary data from comparable
existing casinos, data from comparable casino jurisdictions, and
proprietary consultant databases constructed through many years of
access to casinos players clubs and other databases. Consequently, a
casinos ability to attract visitations and spending can be reasonably
estimated using gravity models, which incorporate data on the number of
people living at different distances from an existing or proposed
casino. However, we want to suggest that some important modifications to
these models could improve their performance and may be necessary going
forward in the industry. In this respect, the function and complexity of
gravity models in the casino industry has already undergone at least
three phases of development, with the most recent phase requiring that
we reconsider how to measure the gravity factor - or mass - of casinos.

The first phase of gravity modeling in the casino industry was the
period of its greatest expansion (1976-1999), beginning with the opening
of casinos in Atlantic City and culminating with the opening of three
commercial casinos in Detroit, Michigan. During this phase, casinos were
opening in new jurisdictions, often with limited entry restrictions
designed to protect new operators, so gravity models were comparatively
simple efforts to measure the potential revenue that would be captured
by casinos, including the percentage of revenues and visitors that would
be captured from out-of-state or out-of-region visitors (Eadington,
1995; 1998; Hsu, 1999, chaps. 5-8; Walker, 2007, Chap. 2-4; Meister,
Rand, and Light, 2009).

The second phase of gravity modeling has revolved around later
entrants to the expanded gaming movement, including new expansions, such
as New York, Pennsylvania, Delaware, Maryland, Massachusetts, Maine, and
Ohio (2005 -2012), where gravity modeling has focused more on the
ability of local or regional facilities to recapture visitors and
revenues from adjacent states (Barrow and Borges, 2010; Dense and
Barrow, 2003; McGowan, 2009). This has meant that location (distance)
and mass have become more important to estimating a casinos probability
of success in the political terms that now structure expanded gaming
debates. It also means that gravity models have become increasingly
complex, or confronted with increasing difficulties in measuring the
comparative impact of different facilities in increasingly congested
market areas. Moreover, as expanded gaming debates have shifted from
capturing revenues from adjacent states to recapturing revenues being
lost to adjacent states, it has raised an additional question for
gravity modelers: What types and size of gaming facilities (i.e., mass)
are necessary to effectively compete with existing gaming facilities in
adjacent states, particularly if the objective is to generate a new
destination as opposed to merely recapturing local convenience gamblers.
This has juxtaposed the question of using multiple small convenience
facilities taxed at high rates to capture convenience gamblers (e.g.,
Pennsylvania) against the construction of resort casinos designed to
generate new destinations and bolster the larger tourism and hospitality
industry (e.g., Massachusetts).

Finally, it appears that gravity modeling is about to enter a third
phase of development as expanded gaming reaches maturity, but new market
entrants either seek to enter saturated or nearly saturated markets at
lower operating margins or they seek to displace existing venues by
constructing more elaborate facilities with a higher gravity factor.
This debate is already surfacing in a number of U.S. jurisdictions and
it means that the problem of measuring mass is becoming even more
important in the construction of gravity models for the casino industry.

First, Fluff models require investigators to have reliable survey
data on the propensity to gamble at different distances from a casino,
data from comparable facilities (e.g., players club databases), or it
requires one to make reasonable assumptions about the distance decay
factor, which theoretically declines exponentially at regular distances
from a central place (e.g., 30 minutes). However, with the onset of the
Great Recession in late 2007, the overall propensity to gamble declined
in all of the New England states, as elsewhere in the country, which is
directly related to rising unemployment, decreases in disposable
personal income, increased savings rates, and declining home values. The
general principle of distance decay remained intact during the Great
Recession, but the propensity to gamble decreased across-the-board,
which for the first time, has forced gravity modelers to recognize that
propensity factors are not fixed by time or place, but can shift upwards
or downwards significantly depending on the macro-level economy (Barrow
and Borges 2007a; 2007b; 2009; 2011; 2013). These assumptions need to be
recalibrated, at least for the time being, and in the future it must be
recognized that the propensity to gamble will likely be cyclical in
nature, especially once a gaming market reaches saturation.

Second, the mass of a retail shopping center was traditionally
measured in square feet, but Huff offered persuasive arguments that
square footage was really a proxy for the range of merchandise offerings
and the range of choices available to consumers. The number and range of
retail offerings in the case of casinos is a function of gaming space,
gaming positions, and the range of non-gaming amenities. The size of a
gaming facility can be measured in square feet of gaming space, or the
number of gaming positions, but another significant determinant of mass
is also the basis of the distinction between destination resort casinos
and convenience gaming facilities, which have significantly different
amounts of gravitational force.

A major lacuna in the standard gravity model, as applied to
casinos, is that gaming positions are not the only measure of a casinos
mass. A resort casino's mass and, therefore, its gravitational
force is also a function of its range of games, which typically include
table games and poker and it is not clear that one table equals six slot
machines, because tables may attract a fundamentally different type of
customer (Barrow and Borges, 2013). Thus, the availability of table
games and the number of table games needs to be accounted for and
weighted separately from slot machines. A casino with table games will
necessarily attract a new cohort of players simply because slot parlors
do not offer table games so it does not make sense to assume that 60
additional slot machines has the same weight as ten table games in
calculating a gravity factor.

Furthermore, many gamblers are seeking an entertainment experience
that includes more than just gambling or one that generates a different
general atmosphere. Thus, a resort casino's gravity is also a
function of its non-gaming amenities. In 2012, for example, the New
England Gaming Behavior Survey (Barrow and Borges, 2013) found that 69%
of the individuals from Rhode Island, Massachusetts, New Hampshire, and
Maine who visited Foxwoods Resort or Mohegan Sun in the previous twelve
months did not visit either Twin River or Newport Grand in Rhode Island,
despite their closer functional distance to these population centers.
Furthermore, the non-gaming component of casino entertainment complexes
is becoming increasingly important to a casino's competitiveness.
In New England, the percentage of visitors to Foxwoods Resort and
Mohegan Sun, who report that they rarely or never gamble has increased
from 8% in 2006 to 22% in 2012 (Barrow and Borges, 2007a, p. 15; 2013,
p. 12). The American Gaming Associations (2013, pp. 3, 27-28) most
recent survey of American gamblers finds that 26% of casino visitors
nationwide report that they rarely or never gamble. Thus, it is clear
that non-gaming amenities need to be incorporated into the calculation
of gravity factors in some manner and to some significant extent. These
amenities include parking spaces, hotel rooms, conference and meeting
facilities, restaurants and bars, live entertainment venues, dance
clubs, spas, RV parks, and golf courses. The authors agree that the
exact weighting of non-gaming amenities is a matter for further
discussion, but the magnitude of this difference could theoretically
shift the breaking point and related probabilistic contours of a casino
to a significant degree when assessing competitive impacts on existing
facilities.

Finally, the evolution of casinos from gambling parlors to regional
entertainment complexes and tourism attractions means that the problem
of the tourist factor needs to be addressed in some explicit way. It
appears that most gravity modelers, including the authors, when
confronted with this problem simply choose a percentage add-on to the
base gravity model, such as a 10% or 20% increment to gross gaming
revenues. However, a more accurate tourism factor will require better
local and regional tourism data (which is often quite sketchy), surveys
of the gaming interests of tourists, and analysis of the increasing role
of casinos in attracting tourists, conventions, and business travelers.
(5)

The claim that gravity models need to incorporate non-gaming
amenities when forecasting the potential revenues or competitive impact
of new and existing casinos is also grounded in earlier critiques of
gravity modeling, such as those by Cox (1959), Bucklin (1967), and Black
(1983), who suggest that consumers make choices based on the aggregate
utility or aggregate convenience of competing options. Louis P. Bucklin
(1967, 37) notes that the earliest gravity models generally used a
single variable such as population or retail square footage (or gaming
positions) as a proxy for mass, although more recent research on
consumer behavior confirms the importance of mass in shifting the
consumer's ideal breaking point (DeSarbo, Choi, and Spaulding,
2002) and, therefore, the importance of defining it accurately. William
Black (1983, pp. 18-19) has also called on scholars to more precisely
specify and measure "the attractiveness component" of retail
mass through the use of multiple attractiveness measures, which is what
we propose by incorporating table games and non-gaming amenities into
casino gravity models. For casinos, these factors may also include
physical appearance, cleanliness, safety, luxury, the availability of
different games, various types of food and beverage outlets, gaming
floor service, employee friendliness, the surrounding vicinity, and
brand name. However, a gravity model cannot specify or quantify these
factors in any objective manner without additional locally specific
research on gambling behavior and this continues to be a limitation of
gravity models (Thompson, f963).

More importantly, however, these limitations have three major
implications for public and private decision-makers. First, as the
casino market approaches maturity, and even saturation in some
jurisdictions, there will continue to be proposals to move casinos
closer to population and income centers. These new facilities will
negatively impact existing casinos and traditional gravity models will
likely understate that negative effect, particularly since the new trend
is toward more and more elaborate non-gaming amenities. Thus, there is
the potential to understate job losses and tax revenue losses at
existing facilities and, thereby, overstate the net economic and fiscal
benefits of new casinos in some jurisdictions. Furthermore, new
operators entering saturated markets will have a vested interest in
understanding their negative impacts on existing facilities to gain
approval for their facilities and, hence, there may be pressure on the
industry's consultants to retain the standard gravity model even
when it is not the most accurate tool for evaluating economic and fiscal
impacts.

Another difficulty in evaluating the impact of proposed new
facilities in congested markets is that gravity models were originally
designed to measure the comparative gravity of two competing regions or
facilities. However, as the distance between casinos shrinks in
congested and saturated markets, gravity modelers confront the di.culty
of evaluating multiple overlapping market areas, which the traditional
contour map has difficulty representing and which the standard gravity
model has difficulty processing as new exponents overlap with already
overlapping exponents. One can simply assign market share to a cluster
of facilities based on gravity factors, but this requires more accurate
gravity factors and it also evades the problem of the quality of travel
networks and location (direction of travel) in selecting a casino.

Second, state gambling policies have been shifting from an emphasis
on revenue generation to an emphasis on job creation and this further
shifts the emphasis from slot machines to table games and to non-gaming
amenities (Barrow, 2012). At the same time, as casino markets become
more competitive, and slot machines become a widely available commodity,
existing casinos are making the decision internally to add more
non-gaming amenities, such as hotels, outlet malls, RV parks, convention
centers and meeting space, golf courses, bowling alleys, concert halls,
and sporting arenas to differentiate themselves from other gaming
venues. These items increase the gravity of existing casinos and, thus,
bring more visitors to an existing casino, including more employees.
However, as local and state government officials have become more
sophisticated in their economic development policies, they are seeking
impact fees, infrastructure and public safety mitigation funds, revenue
sharing, etc. Once again, casino operators have a vested interested in
understanding these impacts by relying on existing gravity models that
understate visitations and impacts.

Finally, these considerations could substantially affect
policymakers' decisions on whether to authorize new facilities
(both commercial and Indian), the size and type of facilities, and the
location of new facilities (i.e., distance and spacing requirements).
These issues are already surfacing in many jurisdictions and,
consequently, the theoretical limitations of gravity modeling present
the industry and its regulators with a practical policy issue that is
likely to intensify with time and that will put gravity models at the
center of these debates.

Evart, C., Treptow, R. and Zeitz, C. (1997). Selecting a gaming
developer: Guidelines for municipal governments. In Eadington, W.R. and
Cornelius, J.A. (eds.), Gambling: Public policies and the social
sciences. Reno: Institute for the Study of Gambling and Commercial
Gaming, University of Nevada, Reno, pp. 423-40.

Evenett, S.J. and Keller, W. (2002). On theories explaining the
success of the gravity equation. Journal of Political Economy, 110(2),
281-316.

Williams, J. (1997). The casino bid process: Some questions
answered. In W.R. Eadington and J.A. Cornelius, (eds.), Gambling: Public
policies and the social sciences. Reno: Institute for the Study of
Gambling and Commercial Gaming, University of Nevada, Reno, pp. 393-405.

Endnotes

(1) The earliest pre-Reilly "gravity models" were
pioneered by chain tobacco shops attempting to identify the volume,
composition, and quality of pedestrian traffic in different locations to
scientifically identify the best and most profitable locations for
opening tobacco stores. Oil companies later applied the same research
technique to automobile traffic as the basis for identifying sites for
gasoline stations (Applebaum 1965, p. 234).

(2) For a critical analysis of the empirical evidence used in
formulating the Law of Retail Gravitation, see (Schwartz, 1962).

(3) Mass factors into convenience, because if a slot machine player
repeatedly finds that a local casino's gaming devices are occupied,
and that there is a long wait time to find a position at their preferred
device, they will often be willing to travel a longer distance to a
larger facility to insure that a position is available, since the
"time to position" (i.e., drive plus wait) is essentially the
same or shorter, despite the longer initial drive-time.

(4) In a more recent example, Spectrum Gaming Group prepared a 2011
market feasibility analysis which found that three destination resort
casinos in South Florida would generate $1 billion in tax revenue for
the State of Florida. Flowever, in a more study prepared for the Florida
Legislature (2013), it would find that "wide open" gaming--33
casinos and six destination resorts--would cause the state to lose $22
million a year. When queried about the significant difference in
results, the official response was "different assumptions"
about tourist visits, with the former study's estimates assuming
"a massive marketing plan aimed at Asians" and the promise
that one of the casino operators "would hire private planes to
ferry customers to the region" (quoted in Kam, 2013; see also,
Spectrum Gaming Group, 2013).